Math Toolkit

1
Math Toolkit

• The Support System to Physics

2
Units of Measure

• There are two basic units of measure found in the
  natural world(read the United States)
• US system based on self indulgent scientists
• Metric System Based on the powers of 10

3
Fundamental Units

• Time - sec

• Length - m

Mass - kg

• cm, mm, km
• Astrological units distance from earth to
  sun
• Light Year distance traveled
  by light in a year
• Inches, feet (ungainly)

• Day, week, hour, year

Pounds, Tons We will stick with these base
units throughout the year.
These three fundamental units L, T, M can be used
to derive almost all measurements used in this
class.
4
Derived Units

• Combinations of the fundamental units to more
  useful measurements

• Speed
• Volume
• Density
• Acceleration

5
Dimensional Analysis

• If you drop an ball from a certain height and
  then change that height what happens to the time?

6
Error the forgotten step-child of calculations

• Accuracy vs Precision
• Accuracy how well the results agree with the
  standard value how close they were to the answer
  (in true field testing this is impossible to tell
  since the answer is unknown)
• Precision how exact the measurements were to
  one another great precision will look good on
  paper but without accuracy I will award you no
  points and may god have mercy on your soul

7
Uncertainty

• Any measurement you make is meaningless without
  the knowledge of its uncertainty
• A measure of the amount of error that is made
  when measuring an event

8
The SI prefix system

• Femto . . . . . . . . . . . . . . . . .
• Pico . . . . . . . . . . . . . . . . . . .
• Nano . . . . . . . . . . . . . . . . . .
• Micro . . . . . . . . . . . . . . . . . .
• Milli . . . . . . . . . . . . . . . . . . .
• Centi . . . . . . . . . . . . . . . . . .
• Deci . . . . . . . . . . . . . . . . . . .
• Kilo . . . . . . . . . . . . . . . . . . .
• Mega . . . . . . . . . . . . . . . . . .
• Giga . . . . . . . . . . . . . . . . . . .
• Tera . . . . . . . . . . . . . . . . . . .

• 10-15
• 10-12
• 10-9
• 10-6
• 10-3
• 10-2
• 10-1
• 103
• 106
• 109
• 1012

9
Significant Figures

• Number of non-zero digits
• Number of trapped zeros
• Any trailing zeros after the non-zeros with the
  presence of a decimal

10
Sig Figs in Problems

• Addition/ Subtraction
• Least number of decimal places

• Multiplication/Division
• Least number of significant places

Your answer cannot be more precise than the
values used to evaluate it
11
Graphing Data

• See Excel Spreadsheet

12
Types of Relationships

• Just Friends
• Linear ymxb
• Quadratic yax2bxc
• Inverse ya/x